arXiv subjects
Publications and source records attributed to Urs M. Heller.
We present results of quenched $SU(3)$ hadron spectroscopy using $\order(a)$ improved Wilson fermions. The configurations were generated using an $\order(a^2)$ improved 6-link $SU(3)$ pure gauge action at $β$'s corresponding to lattice spacings of $0.43$, $0.25$, $0.20$, $0.18$, and $0.15$ fm. We find evidence that fermionic scaling violations are consistent with $\order(a^2)$ errors.
We present new results in an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover, an important indicator of continuum scaling, a determination of the induced baryon charge and baryon susceptibility, used to study the dissolution of hadrons at the crossover, the scalar susceptibility, a signal for the appearance of soft modes, and the chiral order parameter, used to test models of critical behavior.
Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios are presented. High statistics quenched runs at $β=5.7$, $5.85$, $6.0$, and $6.3$, plus a run still in progress at $β=6.52$ make possible a preliminary extrapolation to the continuum. The data allows good control of all systematic errors except for quenching, although not all of the error estimates have been finalized. Results from configurations which include effects of dynamical quarks show a significant deviation from the quenched results and make possible a crude estimate of the quenching error.
We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrtσ / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint with the continuum limit there being a $ϕ^4$ theory with a diverging correlation length only in the $0^{++}$ channel.
We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrtσ / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint, with the continuum limit there being a $ϕ^4$ theory with a diverging correlation length only in the $0^{++}$ channel. We comment on the implications for the scaling behavior along the fundamental or Wilson axis.
We determine the mass and decay constant of the $a_1$ meson using Monte Carlo simulation of lattice QCD. We find $M_{a_1} = 1250 \pm 80$ MeV and $f_{a_1} = 0.30 \pm 0.03 ~({\rm GeV})^2$, in good agreement with experiment.
We study the gluon propagator in Landau gauge in the deconfined phase of $SU(2)$ gauge theory. From the long-distance behaviour of correlation functions of temporal and spatial components of the gauge fields we extract electric ($m_e$) and magnetic ($m_m$) screening masses. For temperatures larger than twice $T_c$ we find no additional temperature dependence in $m_e(T)/T$, while $m_m(T)/T$ drops with increasing temperature. The decrease is consistent with the expected behaviour, $m_m(T) \sim g^2(T)T$. We find $m_e(T) = 2.484(52)T$ and $m_m(T) = 0.466(15) g^2(T) T$.
Preliminary results from the MILC collaboration for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios are presented. We compute in the quenched approximation at $β=6.3$, 6.0 and 5.7 with Wilson light quarks and static and Wilson heavy quarks. We attempt to quantify all systematic errors other than quenching, and have a first indication of the size of quenching errors.
We investigate a version of SU(2) lattice gauge theory with a logarithmic action. The model is found to exhibit confinement, contrary to previous claims in the literature. Comparing ratios of physical quantities, like $\sqrtσ/T_c$, we find that the model belongs to the same universality class as the standard SU(2) lattice gauge theory with Wilson action. Like the positive plaquette model, the model with logarithmic action has a monotonic $β$-function, without the famous dip exhibited by the Wilson action. Short distance dislocations affecting the definition of topology are slightly more suppressed than for the positive plaquette model.
We test the cooling algorithm with gluonic and staggered hadronic spectroscopy on $SU(3)$ gauge field configurations generated with two flavors of staggered dynamical fermions. We find cooling is not reliable as the basis for improved hadronic operators. We also find that performing cooling sweeps to reveal more clearly the topological properties of the gauge fields eliminates the spin structure of the hadron spectrum.
We study the thermal phase diagram of pure SU(3) lattice gauge theory with fundamental and adjoint couplings. We improve previous estimates of the position of the bulk transition line and determine the thermal deconfinement transition lines for $N_t=2,4,6,$ and 8. The endpoint of the bulk transition line $(β_f, β_a)=(4.00(7), 2.06(8))$ improves upon earlier estimates obtained using smaller lattice sizes. For $N_t > 4$ the deconfinement transition line splits cleanly away from the bulk transition line. With increasing $N_t$ the thermal deconfinement transition lines shift to increasingly weaker coupling, joining onto the bulk transition line at increasingly larger $β_a$ in a pattern consistent with the usual universality picture of lattice gauge theories. We also discuss the possible consequences of an induced adjoint term from the fermionic determinant and determine this induced term numerically with a microcanonical demon method for two flavors of dynamical Wilson fermions.
We study the thermal phase diagram of pure SU(3) gauge theory with fundamental and adjoint couplings. We improve previous estimates of the position of the bulk transition line and determine the thermal deconfinement transition lines for $N_t=2,4,6,$ and 8. For $N_t > 4$ the deconfinement transition line splits cleanly away from the bulk transition line. With increasing $N_t$ the thermal deconfinement transition lines shift to increasingly weaker coupling, joining onto the bulk transition line at increasingly larger $β_a$ in a pattern consistent with the usual universality picture of lattice gauge theories.
The status of the triviality bound of the Higgs mass in the Minimal Standard Model is reviewed. It is emphasized that the bound is obtained, in the scalar sector, by limiting cutoff effects on physical processes. Results from several regularization schemes, including actions that allow a parameterization and tuning of the leading cutoff effects, are presented. They lead to the conclusion that the Minimal Standard Model will describe physics to an accuracy of a few percent up to energies of the order 2 to 4 times the Higgs mass, $M_H$, only if $M_H \le 710 \pm 60 ~ GeV$. The status of Higgs and fermion mass bounds in Higgs-fermion models is also briefly reviewed.
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of 2-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-$N$ partition function zeros in the complex plane.
A brief review of the role of the Higgs mechanism and the ensuing Higgs particle in the Minimal Standard Model is given. Then the property of triviality of the scalar sector in the Minimal Standard Model and the upper bound on the Higgs mass that follows is discussed. It is emphasized that the bound is obtained by limiting cutoff effects on physical processes. Actions that allow a parameterization and tuning of the leading cutoff effects are studied both analytically, in the large $N$ limit of the generalization of the $O(4)$ symmetry of the scalar sector to $O(N)$, and numerically for the physical case $N = 4$. Combining those results we show that the Minimal Standard Model will describe physics to an accuracy of a few percent up to energies of the order 2 to 4 times the Higgs mass, $M_H$, only if $M_H \le 710 \pm 60 ~ GeV$. This bound is the result of a systematic search in the space of dimension six operators and is expected to hold in the {\it continuum}. (Complete postscript file can be obtained by anonymous ftp from ftp.scri.fsu.edu as file "corfu_92.ps" from directory "pub/heller".)
We describe recent results concerning the behavior of lattice QCD with light dynamical Wilson and Staggered quarks. We show that it is possible to reach regions of parameter space with light pions $m_π\approx 0.2/a$ using Wilson fermions. If the Hybrid Molecular Dynamics (HMD) algorithm is used with the same parameters it gives incorrect results. We also present preliminary results using a higher-order integration scheme.
We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff effects at four percent in several regularized models with tunable couplings in the bare action yield triviality bounds displaying a large degree of universality. Extrapolating from $N=\infty$ to $N=4$ we conservatively estimate that a Higgs particle with mass up to $0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff effects, indicating that strong scalar self interactions in the standard model are not ruled out. We also present preliminary numerical results of the physical $N=4$ case for the $F_4$ lattice that are in agreement with the large $N$ expectations. Note: The full ps file is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lat92_proc.ps (to get it type: get lat92_proc.ps)
We calculate the triviality bound on the Higgs mass in scalar field theory models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial} \approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity. Limits on observable cutoff effects at four percent in several regularized models with tunable couplings in the bare action yield triviality bounds displaying a large degree of universality. Extrapolating from $N=\infty$ to $N=4$ we conservatively estimate that a Higgs particle with mass up to $0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff effects, indicating that strong scalar self interactions in the standard model are not ruled out. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called lrg_n_hig.ps (to get it type: get lrg_n_hig.ps)